What are possible values of x if #ln(x-4) +ln(3) <=0#?

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Answer 1 · 2018-05-14T04:39:58

Possible values of #x# are given by #4< x<=13/3#

We can write #ln(x-4)+ln3<=0# as

#ln(3(x-4))<=0#

graph{lnx [-10, 10, -5, 5]}

Now as #lnx# is a function which always increases as #x# increases (graph shown above) as also that #ln1=0#, this means

#3(x-4)<=1#

i.e. #3x<=13#

and #x<=13/3#

Observe that as we have #ln(x-4)# domain of #x# is #x>4#

Hence possible values of #x# are given by #4< x<=13/3#